The size of Mandelbrot bulbs

A. C. Fowler; M. J. McGuinness

doi:10.1016/j.csfx.2019.100019

The size of Mandelbrot bulbs

A. C. Fowler, M. J. McGuinness

Department of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

We provide an analytic estimate for the size of the bulbs adjoining the main cardioid of the Mandelbrot set. The bulbs are approximate circles, and are associated with the stability regions in the complex parameter μ-space of period-q orbits of the underlying map z→z²−μ. For the (p, q) orbit with winding number p/q, the associated stability bulb is an approximate circle with radius [Formula presented].

Original language	English
Article number	100019
Journal	Chaos, Solitons and Fractals: X
Volume	3
DOIs	https://doi.org/10.1016/j.csfx.2019.100019
Publication status	Published - Sep 2019

Keywords

Mandelbrot bulbs
Mandelbrot set

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10.1016/j.csfx.2019.100019

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title = "The size of Mandelbrot bulbs",

abstract = "We provide an analytic estimate for the size of the bulbs adjoining the main cardioid of the Mandelbrot set. The bulbs are approximate circles, and are associated with the stability regions in the complex parameter μ-space of period-q orbits of the underlying map z→z2−μ. For the (p, q) orbit with winding number p/q, the associated stability bulb is an approximate circle with radius [Formula presented].",

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AB - We provide an analytic estimate for the size of the bulbs adjoining the main cardioid of the Mandelbrot set. The bulbs are approximate circles, and are associated with the stability regions in the complex parameter μ-space of period-q orbits of the underlying map z→z2−μ. For the (p, q) orbit with winding number p/q, the associated stability bulb is an approximate circle with radius [Formula presented].

KW - Mandelbrot bulbs

KW - Mandelbrot set

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DO - 10.1016/j.csfx.2019.100019

M3 - Article

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JO - Chaos, Solitons and Fractals: X

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ER -

The size of Mandelbrot bulbs

Abstract

Keywords

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